Now, the smallness of the real part of \(x_P\) , 0.07, versus the modulus of its imaginary part, \(0.20\) , implies that the resonance effects of the graviball (as well as those of the \(\sigma \) ) peak in the variable \(s\)  at much lower values than \(\Lambda _U^2\) . This can be explicitly shown by considering the Omnès function \(\Omega ^{(0)}(s)=T^{(0)}/V^{(0)}(s)\equiv D^{(0)}(s)^{-1}\) , whose modulus squared in shown in Fig. REF . Reference [1]} also argued about the numerical suppression of the phase space of multi-graviton states, which for \(s<\Lambda _U^2\)  provides a strong suppression of this type of multi-particle states in the unitarity relation. This is a similar effect to that discussed for \(\pi \pi \)  scattering in Ref. [2]}. Additionally, Ref. [1]} considered the impact of higher-order monomials in the expansion of Eq. (), containing three and four powers of the curvature tensor (and its contraction thereof). The former are indicated by \(\lbrace R^3\rbrace \)  and the latter by \(\lbrace R^4\rbrace \) . It was found in Ref. [4]} that the \(\lbrace R^3\rbrace \)  terms do not contribute to the scattering amplitude \(T_{22,22}\) , while the \(\lbrace R^4\rbrace \)  do. These extra terms give rise to a relative change in the pole position of the graviball of around a 3% [1]}, in agreement with the expected \(x^3=1\%\) .
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